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arXiv · 2410.06559

The pseudometric topology induced by upper asymptotic density

Jonathan M. Keith
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Abstract

Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which $P(\mathbb{N})$ is complete. The collection $D$ of sets with asymptotic density is closed in this pseudometric, and closed subsets of $D$ are characterised by a generalisation of an additivity property (AP0).

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Jonathan M. Keith. 2024-10-09. The pseudometric topology induced by upper asymptotic density. https://arxiv.org/abs/2410.06559

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